When agents observe a continuous variable and a discrete signal based on that variable, theory suggests that the signal should not impact behavior conditional on the variable. Numerous empirical studies, many based on regression discontinuity design, contradict this basic prediction. We propose two rationalizations with testable implications. One is based on information acquisition costs and the other on learning and imperfect information. Using education data from North Carolina and exploiting a pay-for-performance system, we find support for the model of learning. This implies that rational responses to policy interventions may emerge gradually, and evaluations with short-term data may understate treatment effects.

中文翻译：

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当激励过于重要时：解释对不相关信息的重大反应

当代理观察到一个连续变量和一个基于该变量的离散信号时，理论表明该信号不应影响以该变量为条件的行为。许多基于回归不连续设计的实证研究与这一基本预测相矛盾。我们提出了两个具有可测试含义的合理化。一种基于信息获取成本，另一种基于学习和不完善信息。使用来自北卡罗来纳州的教育数据并利用按绩效付费的系统，我们找到了对学习模型的支持。这意味着对政策干预的理性反应可能会逐渐出现，而短期数据的评估可能会低估治疗效果。